The present invention relates to digital-to-analog converters. More particularly, the invention relates to digital-to-analog converters for use in electric servo motor positioners.
The digital input to the digital-to-analog (D/A) converter in electric servo motor positioners represents motor position, while the output of the circuit represents a motor velocity command based on motor position. Because velocity is the first time derivative of position, velocity is proportional to the square root of the position if acceleration and deceleration are to remain constant.
The conventional method of taking the square root of an analog voltage presents significant problems in that the voltages and currents from the least significant bit of a 24 bit D/A converter are much smaller than the noise and offset voltages and currents of the operational amplifier in the current-to-voltage converter. Additionally, the dynamic range requirements are too great, typically 0.478 .mu.V to 8 V. The required gain for the square root amplifier is also too great, typically 4096. Further, because a motor positioner may operate over thousands of revolutions with 4096 discrete positions within a revolution, a 24 bit (16.7 million) dynamic range is required with very high accuracy near zero.
The extreme dynamic range requirements of the 24-bit converter of 0.5 microvolts per bit followed by the extremely high gain requirements of the square-root amplifier (greater than 4000 near zero) make a conventional circuit topology very expensive, if not impossible to implement.